Question

. Two regular polygons are such that the ratio between their number of sides
is 1 : 3 and the ratio of the measures of their interior angles is 3 : 4. Find the
number of sides of each polygon.​

Answer 1

Answer:

Let number of sides of two polygons are n and 2n

measures of interior angles of x sided regular polygon is

x

(x−2)×180°

so

n

n−2

×180°

2n

2n−2

×180°

=

3

4

⇒

2(n−2)

2n−2

=

3

4

⇒6n−6=8n−16

⇒2n=10

⇒n=5

Therefore, number of sides of polygon are 5 and 10.